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If a wire is bent into the shape of a square, then the area of the square is 81 cm². When wire is bent into a semi-circular shape, then the area of the semi-circle will be
Prepare for Class 10th Maths using NCERT solutions and MCQ-based questions from Chapter 11: Areas Related to Circles. Practice exercise questions, short-answer problems and clear explanations to master concepts like areas of sectors, segments and combinations of plane figures. These resources are designed as per the CBSE syllabus for effective exam preparation. Consistent practice will sharpen your problem-solving skills and help you excel in board exams. Utilize step-by-step solutions and revision notes crafted to simplify complex ideas and ensure success. Focus on understanding the formulas and their applications to build a strong foundation. Begin solving now to achieve excellent results and secure higher marks in exams. Start today!
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Given:
– Area of square = 81 cm² ⇒ Side = √81 = 9 cm.
– Perimeter of square = 4 × 9 = 36 cm (length of wire).
For semi-circle:
– Perimeter = πr + 2r = 36 ⇒ r(π + 2) = 36.
– Substitute π = 22/7: r(22/7 + 2) = 36 ⇒ r(36/7) = 36 ⇒ r = 7 cm.
Area of semi-circle:
– Area = (1/2)πr² = (1/2)(22/7)(7²) = (1/2)(22)(7) = 77 cm².
This question pertains to Chapter 11 of the Class 10th NCERT Mathematics textbook, titled “Areas Related to Circles.” Answer the question based on your comprehension of the chapter.
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